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A MINLP model for the rigorous design of shell and tube heat exchangers using the TEMA standards

CHEMICAL ENGINEERING RESEARCH & DESIGN 2007年第A10期85卷 1423-1435页

作者： Ravagnani, M. A. S. S. Caballero, J. A. Univ Estadual Maringa DEQ PEQ CTC UEM BR-87030900 Maringa Parana Brazil Univ Alicante Dept Chem Engn E-03080 Alicante Spain

In this paper a mixed integer non-linear programming (MINLP) model is proposed for the design of shell and tube heat exchangers. The model rigorously follows the TEMA (Tubular Exchanger Manufacturers Association) Standards and Bell-Delaware Method is used to the shell side calculations. Mechanical design features (shell and tube bundle diameters, internal and external tube diameters, tubes length, pitch and tube arrangement, number of tubes and tube passes) and thermal-hydraulic variables (heat, area, individual and overall heat transfer coefficients, shell and tube pressure drops and fouling) are variables to be optimized. The equipment is designed under pressure drop and fouling limits. Three cases from the literature are studied, with two different objective functions, considering just the heat transfer area minimization or the annual cost minimization, including area and pumping expenses. More realistic values are obtained when compared with the literature, considering fouling and pressure drop effects according to TEMA Standards.

关键词： TEMA standards optimization heat exchanger design mixed integer non linear programming generalized disjunctive programming mathematical programming

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A modeling strategy for integrated batch process development based on mixed-logic dynamic optimization

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COMPUTERS & CHEMICAL ENGINEERING 2016年 94卷 287-311页

作者： Moreno-Benito, Marta Frankl, Kathrin Espuna, Antonio Marquardt, Wolfgang UCL Ctr Proc Syst Engn Torrington Pl London WC1E 7JE England Rhein Westfal TH Aachen Proc Syst Engn Turmstr 46 D-52056 Aachen Germany Univ Politecn Cataluna Dept Chem Engn ETSEIB Av Diagonal 647 E-08028 Barcelona Spain

This paper introduces an optimization-based approach for the simultaneous solution of batch process synthesis and plant allocation, with decisions like the selection of chemicals, process stages, task-unit assignments, operating modes, and optimal control profiles, among others. The modeling strategy is based on the representation of structural alternatives in a state-equipment network (SEN) and its formulation as a mixed-logic dynamic optimization (MLDO) problem. Particularly, the disjunctive multistage modeling strategy by Oldenburg and Marquardt (2008) is extended to combine and organize single-stage and multistage models for representing the sequence of continuous and batch units in each structural alternative and for synchronizing dynamic profiles in input and output operations with material transference. Two numerical examples illustrate the application of the proposed methodology, showing the enhancement of the adaptability potential of batch plants and the improvement of global process performance thanks to the quantification of interactions between process synthesis and plant allocation decisions. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Batch process synthesis Plant allocation Dynamic optimization generalized disjunctive programming Synchronization Multistage modeling

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Design optimization of shell and tube heat exchangers sizing with heat transfer enhancement

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COMPUTERS & CHEMICAL ENGINEERING 2020年 137卷 106821-106821页

作者： Yang, Zekun Ma, Yingjie Zhang, Nan Smith, Robin Univ Manchester Ctr Proc Integrat Sch Chem Engn & Analyt Sci Manchester M13 9PL Lancs England

Heat transfer enhancement (HTE) is an efficient technology to improve the performance of shell and tube heat exchangers (STHEs). While there exist many commercial software packages, heat exchanger design still highly depends on users' experiences, resulting in long computing time and inferior solutions. Therefore, a systematic optimization methodology is required in order to achieve an efficient and accurate design solution. This paper presents a generalized disjunctive programming (GDP) model for the optimization of STHE design. It is formulated as a mixed integer non-linear programming (MINLP) problem, involving selection for 12 technology combinations (four tube-side techniques, three shell-side techniques), and all discrete decisions for each selection are modeled by disjunctions. The model is then applied to minimize the total capital cost. Both global optimization solver BARON, and general MINLP solver DICOPT are tested. The results show that the developed method provides a better design solution compared with conventional STHE design procedures. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Mathematical optimization Heat transfer enhancement Shell and tube heat exchanger design generalized disjunctive programming

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Robust Topology Engineering in Multiradio Multichannel Wireless Networks

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IEEE TRANSACTIONS ON MOBILE COMPUTING 2012年第3期11卷 492-503页

作者： Hua, Cunqing Zheng, Rong Zhejiang Univ Dept Informat Sci & Elect Engn Inst Informat & Commun Engn Hangzhou 310027 Zhejiang Peoples R China Univ Houston Dept Comp Sci Houston TX 77204 USA

Topology engineering concerns with the problem of automatic determination of physical layer parameters to form a network with desired properties. In this paper, we investigate the joint power control, channel assignment, and radio interface selection for robust provisioning of link bandwidth in infrastructure multiradio multichannel wireless networks in presence of channel variability and external interference. To characterize the logical relationship between spatial contention constraints and transmit power, we formulate the joint power control and radio-channel assignment as a generalized disjunctive programming problem. The generalized Benders decomposition technique is applied for decomposing the radio-channel assignment (combinatorial constraints) and network resource allocation (continuous constraints) so that the problem can be solved efficiently. The proposed algorithm is guaranteed to converge to the optimal solution within a finite number of iterations. We have evaluated our scheme using traces collected from two wireless testbeds and simulation studies in Qualnet. Experiments show that the proposed algorithm is superior to existing schemes in providing larger interference margin, and reducing outage and packet loss probabilities.

关键词： Wireless networks topology engineering generalized disjunctive programming generalized Benders decomposition

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Modeling issues and implementation of language for disjunctive programming

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COMPUTERS & CHEMICAL ENGINEERING 2000年第9-10期24卷 2143-2155页

作者： Vecchietti, A Grossmann, IE Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA UTN Fac Reg Santa Fe INGAR Inst Desarrollo & Diseno Santa Fe NM USA

This paper describes a number of key modeling issues for the development of tools for solving nonlinear discrete/continuous problems where logic/disjunctive constraints are included in the formulation. A generalized hybrid representation of these problems is presented. A comparison between Constraint logic programming (CLP) and generalized disjunctive programming (GDP) is established together with several constraint transformations from CLP to GDP. The components and expressions of a modeling language for setting up disjunctions and logic constraints are proposed. The language allows the specification of problems with complex logic formulations. A parser is developed for the analysis and translation of the logic sentences into files ready to be used by the solvers. An overview of the solution algorithms is also given together with several aspects about the implementation as a superset of GAMS mathematical programming language. Examples illustrating the capabilities of the proposed system are described. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： generalized disjunctive programming mixed-integer nonlinear programming constraint logic programming modeling language

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A review of the state of the art in optimization

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REVISTA IBEROAMERICANA DE AUTOMATICA E INFORMATICA INDUSTRIAL 2007年第1期4卷 5-+页

作者： Caballero, Jose A. Grossmann, Ignacio E. Univ Alicante Dept Chem Engn E-03080 Alicante Spain Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

This paper presents a review of the most important optimization techniques: linear and nonlinear programming with and without discrete variables and of the algorithms available, to the date, for solving those problems. Besides an extension to deal with problems formulated in terms of disjunctions and logical relationships, deterministic and stochastic global optimization and optimization in problems without a define structure is included together with a general view of the algebraic modelling systems. Copyright (C) 2007 CEA-IFAC.

关键词： optimization LP NLP MINLP MILP generalized disjunctive programming global optimization

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An integration of algal biofuel production planning, scheduling, and order-based inventory distribution control systems

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BIOFUELS BIOPRODUCTS & BIOREFINING-BIOFPR 2019年第4期13卷 920-935页

作者： Nugroho, Yohanes K. Zhu, Liandong Wuhan Univ Sch Resource & Environm Sci 129 Luoyu Rd Wuhan 430079 Hubei Peoples R China Wuhan Univ Hubei Biomass Resource Chem & Environm Biotechnol 129 Luoyu Rd Wuhan 430079 Hubei Peoples R China

This paper studies an integration model of production planning, scheduling, and order- based inventory distribution control systems. It models supply-chain and production dynamics and employs process control to supply-chain operations and the production process and scheduling. It embeds generalized disjunctive programming (GDP) and branch-and-reduce algorithms to obtain an optimal solution. generalized disjunctive programming reformulates the original mixed integer nonlinear programming (MINLP) model and solves the new model with a lower number of integer variables. Afterwards, the branch and reduce algorithm, which is strengthened with outer approximation (OA) cutting planes, is able to find optimal solutions with permissible optimality gaps. The results show that supply network size does not affect forecast accuracy;there is a forecast error rate of 12.9%. Similar figures are also shown for the inventory level, which is expected to be 32% of demand level, production changeover time at 0.58 days, inventory ramp-up period to meet the expected raw materials and final products inventory at 0.02 and 0.04 days respectively, and extra delivery time to meet a certain level of demand change at 1.1 days. The results show that the model is capable of controlling demand forecast, inventory level, and delivery quantity, so that the supply chain can avoid stock out at a minimal level of inventory, regardless of the size of supply-chain networks. (c) 2019 Society of Chemical Industry and John Wiley & Sons, Ltd.

关键词： production planning scheduling process control branch and reduce generalized disjunctive programming mixed integer non-linear programming

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Global optimization algorithm for capacitated multi-facility continuous location-allocation problems

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JOURNAL OF GLOBAL OPTIMIZATION 2018年第4期71卷 871-889页

作者： Lara, Cristiana L. Trespalacios, Francisco Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn 5000 Forbes Ave Pittsburgh PA 15213 USA ExxonMobil Res & Engn Co Corp Strateg Res 1545 Route 22 East Annandale NJ 08801 USA

In this paper we propose a nonlinear generalized disjunctive programming model to optimize the 2-dimensional continuous location and allocation of the potential facilities based on their maximum capacity and the given coordinates of the suppliers and customers. The model belongs to the class of Capacitated Multi-facility Weber Problem. We propose a bilevel decomposition algorithm that iteratively solves a discretized MILP version of the model, and its nonconvex NLP for a fixed selection of discrete variables. Based on the bounding properties of the subproblems, -convergence is proved for this algorithm. We apply the proposed method to random instances varying from 2 suppliers and 2 customers to 40 suppliers and 40 customers, from one type of facility to 3 different types, and from 2 to 32 potential facilities. The results show that the algorithm is more effective at finding global optimal solutions than general purpose global optimization solvers tested.

关键词： Location-allocation problem Weber problem Nonconvex optimization generalized disjunctive programming Mixed-integer nonlinear programming

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Translation of Variables and Implementation of Efficient Logic-Based Techniques in the MINLP Process Synthesizer MIPSYN

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AICHE JOURNAL 2009年第11期55卷 2896-2913页

作者： Ropotar, Marcel Kravanja, Zdravko Univ Maribor Fac Chem & Chem Engn SI-2000 Maribor Slovenia Tanin Sevn Kemicna Ind Dd SI-8290 Sevnica Slovenia

This article describes alternative GDP formulation and convex hull representations for process synthesis problems and their implementation in a unique MINLP process synthesizer MIPSYN. A special translation of variables in mixed-integer, relaxed, and logic-based variations has been proposed, which enables modeling and solving process alternatives in a narrowed lifted space of variables, defined by nonzero lower and upper bounds. Based on these translation variations, alternative formulations have been developed for convex hulls, multiple-term generalized disjunctive programming problems, and logic-based outer-approximation algorithm, all of them being specialized for the synthesis of process flowsheets. Several studies were performed and three different large-scale synthesis problems were solved to test the performance and efficiency of different formulations. This initial research indicates that the proposed alternative convex hull representation usually outperforms the conventional one when solving both MILP and NLP steps in highly combinatorial MINLP process networks problems. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 2896-2913, 2009

关键词： generalized disjunctive programming process synthesis MINLP convex hull translation of variables discrete-continuous translation of variables mixed-integer translation of variables logic-based translation of variables

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Optimization mathematical model for the detailed design of air cooled heat exchangers

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ENERGY 2014年 64卷 734-746页

作者： Manassaldi, Juan I. Scenna, Nicolas J. Mussati, Sergio F. Univ Tecnol Nacl Fac Reg Rosario CAIMI Ctr Aplicac Informat & Modelado Ingn Rosario Santa Fe Argentina INGAR Inst Desarrollo & Diseno CONICET UTN Buenos Aires DF Argentina

This paper presents a disjunctive mathematical model for the optimal design of air cooled heat exchangers. The model involves seven discrete decisions which are related to the selection of the type of the finned tube, number of tube rows, number of tube per row, number of passes, fins per unit length, mean fin thickness and the type of the flow regime. Each discrete decision is modeled using disjunctions, boolean variables and logical propositions. The main continuous decisions are: fan diameter, bundle width, tube length, pressure drops and velocities in both sides of the ACHE, heat transfer area, fan power consumption. Then, the resulting generalized disjunctive programming model is reformulated as a mixed integer non-linear programming, implemented in GAMS (general algebraic modeling system) and solved using a branch-and-bound method. The proposed model was successfully verified by comparing the obtained output results with different designs taken from the literature. Then, the model is solved to obtain the optimal designs corresponding to the following optimization criteria: a) minimization the total annual cost which includes investment (heat transfer area) and operating cost (fan power consumption), b) minimization the heat transfer area and c) minimization the fan power consumption. Obtained optimal and sub-optimal designs are compared in detail. Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.

关键词： Air cooled heat exchangers Optimization generalized disjunctive programming Mathematical programming

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